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Mirrors > Home > ILE Home > Th. List > moan | GIF version |
Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.) |
Ref | Expression |
---|---|
moan | ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 110 | . 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑) | |
2 | 1 | moimi 2103 | 1 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 ∃*wmo 2039 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 |
This theorem is referenced by: moani 2108 mooran1 2110 mormo 2702 rmoan 2952 |
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